One of the big challenges for children with Written Output issues (and/or attention deficit) is beginning their work. It can take a long time to settle down and get started and they can tend to procrastinate with small distractions, but in reality their head may be hopping with ideas and the thought of not being able to output them at the desired rate is a very good explanation of why it's so difficult to start.
It can really help such children if from the outset they have some sense of a time expectation. This can be especially pertinent to children with attention issues for whom the concept of time can feel overwhelming. Therefore I recommend you equip the child with a palm sized kitchen timer and suggest to them you're going to spend 5 mins or 10 mins on x task. You may find the child settles down and begins much swifter because suddenly time has a manageable box around it and the ding or beep of the timer gives them comfort and the confidence to commence. It's important to let the child set and control the timer.
It's especially challenging for children who brains are abuzz with ideas that when they consider it's going to be very difficult to physically get them down on the page, they tend to become discouraged. This will give rise to an unwillingness to commence or a suggestion they don't have any ideas or they can't do it.
I think it can help to have realistic expectations so therefore if the child has a very significant idea they are trying to nail it's better to offer to scribe for them or let them dictate it while you touch type. It's critical to address this sense of ideas being stalled because if you don't, the child can perceive they have no hope of realizing a whole idea on paper. Gradually though with less extensive projects you can negotiate more writing on their end (or typing if they are willing.)
The only way to crack the resistance to writing is to give the child the experience of seeing their ideas materialize. It might help to imagine that for a child with written output troubles it's the equiv of running a long race when you're exhausted having taken two strides.
Ideas can be documented in many, many ways aside from neat paragraphs. If the child is showing acute frustration introduce an alternative such as "a picture with words." On a large sheet of paper they draw a picture and then using single words they can tell the story in the picture. You can then take these single words and build them into sentences and gradually the child can see the idea emerging.
Grab a tape recorder and have the child speak into it. Then the child can in their own time slowly transcribe their idea or story onto the page. This will help relieve some of the pressure and frustration.
Inspiration software is a really great investment. If you cannot afford it, which many families can't, do the same thing with a pencil and paper. Brainstorm words, link ideas and show the child how to form something from nothing. Use devices like multi coloured pens with different ideas. It can help the child to physically switch material. It's makes the consistent act of writing seem less daunting because there's some associated action and decisions to make.
Remember if the child is having a difficult time, get creative rather than insistent.